A Nonlinear Model for Incorporating the Coupled Effects of Surface Energy and Microstructure on the Electromechanical Stability of NEMS

Surface energy and size phenomenon can play significant roles in physical performance of nano-electromechanical systems. Herein, the static and dynamic pull-in behavior of nano-tweezers and nano-switch fabricated from conductive cylindrical nano-wires is studied. The Gurtin–Murdoch surface elasticity in combination with the couple stress theory is employed to incorporate the coupled effects of surface energy and microstructure dependency (size phenomenon). Using Green–Lagrange strain, the higher-order surface stress components are incorporated in the nonlinear governing equation. The effect of gas damping is considered in the model as well as structural damping. The governing equation is solved using the reduced order method. The effects of various parameters on the static and dynamic pull-in parameters, phase plans and stability threshold of the nano-structures are demonstrated.

[1]  Tungyang Chen,et al.  Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids , 2006 .

[2]  R. Rach,et al.  Theoretical modeling of the effect of Casimir attraction on the electrostatic instability of nanowire-fabricated actuators , 2015 .

[3]  Hamid Reza Ovesy,et al.  MODELING THE INFLUENCE OF SURFACE EFFECT ON INSTABILITY OF NANO-CANTILEVER IN PRESENCE OF VAN DER WAALS FORCE , 2013 .

[4]  Randolph Rach,et al.  Modeling the static response and pull-in instability of CNT nanotweezers under the Coulomb and van der Waals attractions , 2013 .

[5]  H. G. Georgiadis,et al.  High-frequency Rayleigh waves in materials with micro-structure and couple-stress effects , 2003 .

[6]  Mohamadreza Abadyan,et al.  Influence of surface effects on size-dependent instability of nano-actuators in the presence of quantum vacuum fluctuations , 2012 .

[7]  N. Pugno,et al.  Nanoelectromechanical Systems: Devices and Modeling , 2006 .

[8]  Liwei Lin,et al.  Electrostatically actuated carbon nanowire nanotweezers , 2009 .

[9]  A. Yousefi-Koma,et al.  Dynamic Analysis of Electrostatically Actuated Nanobeam Based on Strain Gradient Theory , 2015 .

[10]  Jin He,et al.  Surface effect on the elastic behavior of static bending nanowires. , 2008, Nano letters.

[11]  M. Shaat,et al.  Nonlinear-electrostatic analysis of micro-actuated beams based on couple stress and surface elasticity theories , 2014 .

[12]  John Edward Lennard-Jones,et al.  Perturbation problems in quantum mechanics , 1930 .

[13]  G. Rezazadeh,et al.  Micro-inertia effects on the dynamic characteristics of micro-beams considering the couple stress theory , 2014 .

[14]  Alberto Cardona,et al.  On the calculation of viscous damping of microbeam resonators in air , 2009 .

[15]  A. Farrokhabadi,et al.  Effects of size-dependent elasticity on stability of nanotweezers , 2014 .

[16]  Xi-Qiao Feng,et al.  Surface effects on buckling of nanowires under uniaxial compression , 2009 .

[17]  M. Ashby,et al.  Strain gradient plasticity: Theory and experiment , 1994 .

[18]  H. Hosseini-Toudeshky,et al.  Coupled Effect of Surface Energy and Size Effect on the Static and Dynamic Pull-In Instability of Narrow Nano-Switches , 2015 .

[19]  A. Anthoine,et al.  Effect of couple-stresses on the elastic bending of beams , 2000 .

[20]  R. Ansari,et al.  A geometrically non-linear plate model including surface stress effect for the pull-in instability analysis of rectangular nanoplates under hydrostatic and electrostatic actuations , 2014 .

[21]  Baolin Wang,et al.  Influence of surface energy on the non-linear pull-in instability of nano-switches , 2014 .

[22]  Morton E. Gurtin,et al.  A continuum theory of elastic material surfaces , 1975 .

[23]  M. E. Gurtin,et al.  A general theory of curved deformable interfaces in solids at equilibrium , 1998 .

[24]  Jian-Gang Guo,et al.  Dynamic stability of electrostatic torsional actuators with van der Waals effect , 2006 .

[25]  Davide Spinello,et al.  Pull-In Instability in Electrostatically Actuated MEMS due to Coulomb and Casimir Forces , 2008 .

[26]  M. Abadyan,et al.  Modeling Effects of Three Nano-scale Physical Phenomena on Instability Voltage of Multi-layer MEMS/NEMS: Material Size Dependency, van der Waals Force and Non-classic Support Conditions , 2012 .

[27]  P. Tong,et al.  Couple stress based strain gradient theory for elasticity , 2002 .

[28]  Irving H. Shames,et al.  Solid mechanics: a variational approach , 1973 .

[29]  U. Ejike.  The plane circular crack problem in the linearized couple-stress theory , 1969 .

[30]  Ya-Pu Zhao,et al.  Pull-in instability study of carbon nanotube tweezers under the influence of van der Waals forces , 2004 .

[31]  Yiming Fu,et al.  Size-dependent pull-in phenomena in electrically actuated nanobeams incorporating surface energies , 2011 .

[32]  G. Rezazadeh,et al.  Gap Dependent Bifurcation Behavior of a Nano-Beam Subjected to a Nonlinear Electrostatic Pressure , 2014 .

[33]  Mohamadreza Abadyan,et al.  Efficiency of Modified Adomian Decomposition for Simulating the Instability of Nano-electromechanical Switches: Comparison with the Conventional Decomposition Method , 2012 .

[34]  Horacio Dante Espinosa,et al.  EXPERIMENTS AND MODELING OF CARBON NANOTUBE-BASED NEMS DEVICES , 2005 .

[35]  A. Eringen,et al.  On nonlocal elasticity , 1972 .

[36]  Jie Yang,et al.  Nonlinear vibration of nonlocal piezoelectric nanoplates , 2015 .

[37]  H. Haddadpour,et al.  Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano-actuators , 2010 .

[38]  Theresa S. Mayer,et al.  Bottom-up assembly of large-area nanowire resonator arrays. , 2008, Nature nanotechnology.

[39]  M. Porfiri,et al.  Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates , 2008, Sensors.

[40]  S. Asokanthan,et al.  Influence of surface effects on the pull-in instability of NEMS electrostatic switches , 2010, Nanotechnology.

[41]  M. Asghari,et al.  Investigation of the size effects in Timoshenko beams based on the couple stress theory , 2011 .

[42]  Andrew W. Mcfarland,et al.  Role of material microstructure in plate stiffness with relevance to microcantilever sensors , 2005 .

[43]  M. Porfiri,et al.  Review of modeling electrostatically actuated microelectromechanical systems , 2007 .

[44]  Gary F. Dargush,et al.  Couple stress theory for solids , 2011 .

[45]  Mohamadreza Abadyan,et al.  Modeling the effects of size dependence and dispersion forces on the pull-in instability of electrostatic cantilever NEMS using modified couple stress theory , 2011 .

[46]  Fan Yang,et al.  Experiments and theory in strain gradient elasticity , 2003 .

[47]  R. Puers,et al.  A physical model to predict stiction in MEMS , 2006 .